Algebra Readiness Made Easy: Grade 4: An Essential Part of Every Math Curriculum (Best Practices in Action)

Grade 4 NEW YORK • TORONTO • LONDON • AUCKLAND • SYDNEY MEXICO CITY • NEW DELHI • HONG KONG • BUENOS AIRES Algebra Rea...

Author: Mary Cavanagh | Carol Findell | Carole Greenes

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Grade 4

NEW YORK • TORONTO • LONDON • AUCKLAND • SYDNEY MEXICO CITY • NEW DELHI • HONG KONG • BUENOS AIRES Algebra Readiness Made Easy: Grade 4 © Greenes, Findell & Cavanagh, Scholastic Teaching Resources

Scholastic Inc. grants teachers permission to photocopy the activity sheets from this book for classroom use. No other part of this publication may be reproduced in whole or in part, or stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without written permission of the publisher. For information regarding permission, write to Scholastic Inc., 557 Broadway, New York, NY 10012. Editor: Maria L. Chang Cover design by Jason Robinson Interior design by Melinda Belter Illustrations by Teresa Anderko ISBN-13: 978-0-439-83933-4 ISBN-10: 0-439-83933-5 Copyright © 2008 by Carole Greenes, Carol Findell, and Mary Cavanagh All rights reserved. Printed in China. 1 2 3 4 5 6 7 8 9 10

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Algebra Readiness Made Easy: Grade 4 © Greenes, Findell & Cavanagh, Scholastic Teaching Resources

ALGE B

INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

PROBLEM SETS Dog Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 Stamp Stumpers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 Jersey Number . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 Weigh In . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 Balancing Animals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 Where’s My Seat? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

PROBLEM-SOLVING TRANSPARENCY MASTER . . . . . . . . . . . . . 75

SOLVE IT TRANSPARENCY MASTERS . . . . . . . . . . . . . . . . . . . . 76

ANSWER KEY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79

COLOR TRANSPARENCIES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81


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Table of Contents

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ALGE B

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Introduction

Welcome to Algebra Readiness Made Easy! This book is designed to help you introduce students to problem-solving strategies and algebraic-reasoning techniques, to give them practice with major number concepts and skills, and to motivate them to write and talk about big ideas in mathematics. It also sets the stage for the formal study of algebra in the upper grades.

Algebra Standards The National Council of Teachers of Mathematics identifies algebra as one of the five major content areas of the mathematics curriculum to be studied by students in all grades (NCTM, 2000). The council emphasizes that early and regular experience with the key ideas of algebra helps students make the transition into the more formal study of algebra in late middle school or high school. This view is consistent with the general theory of learning—that understanding is enhanced when connections are made between what is new and what was previously studied. The key algebraic concepts developed in this book are: • representing quantitative relationships with symbols • writing and solving equations • solving equations with one variable • replacing unknowns with their values • solving for the values of unknowns • solving two or three equations with two or three unknowns • exploring equality • exploring variables as representing varying quantities • describing the functional relationship between two numbers

Building Key Math Skills NCTM also identifies problem solving as a key process skill and the teaching of strategies and methods of reasoning to solve problems as a major part of the mathematics curriculum for students of all ages. The problem-solving model first described in 1957 by renowned mathematician George Polya has been adopted by teachers and instructional developers nationwide and provides the framework for the problem-solving focus of this book. All the problems contained here require students to interpret data displays—such as text, charts,

4


INTRODUCTION

diagrams, graphs, pictures, and tables—and answer questions about them. As they work on the problems, students learn and practice the following problem-solving strategies: • making lists or cases of possible solutions and testing those solutions • identifying, describing, and generalizing patterns • working backward • reasoning logically • reasoning proportionally The development of problem-solving strategies and algebraic concepts is linked to the development of number concepts and skills. As students solve the problems in this book, they’ll practice counting, computing, applying concepts of place value and number theory, and reasoning about the magnitudes of numbers. Throughout this book, we emphasize the language of mathematics. This language includes terminology (e.g., odd number, variable) as well as symbols (e.g., >, • Digit • Difference • Sum • Even number • Odd number • Factor

Introducing the Problem Set Make photocopies of “Solve the Problem: Jersey Number” (page 33) and distribute to students. Have students work in pairs, encouraging them to discuss strategies they might use to solve the problem. You may want to walk around and listen in on some of their discussions. After a few minutes, display the problem on the board (or on the overhead if you made a transparency) and use the following questions to guide a whole-class discussion on how to solve the problem: • Why is 9 the greatest number on Ima’s list? (Clue 1 shows that when A is added to itself, the sum is less than 20. Since A must be less than 10, then the greatest number that A can represent is 9; 9 + 9 = 18.) • What other numbers are on Ima’s list? (8, 7, 6, 5, 4, 3, 2, 1, and 0) Algebra Readiness Made Easy: Grade 4 © Greenes, Findell & Cavanagh, Scholastic Teaching Resources

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ALGE B

JERSEY NUMBER

READ I RA

Name _____________________________________________ Date __________________ JERSEY NUMBER

SOLVE THE PROBLEM

• Which clue do you think Ima will use next? (Any of the clues will give useful information. If Ima uses Clue 2, she can cross off 0, 1, 2, 3, 4, and 5. That leaves 6, 7, 8, and 9.)

The letter A stands for the number on the jersey. Use the clues to figure out

1) 2)

Work together as a class to answer the questions in “Solve the Problem: Jersey Number.”

Math Chat With the Transparency Display the “Make the Case: Jersey Number” transparency on the overhead. Before students can decide which character is “sharp as a tack,” they need to figure out the answer to the problem. Encourage students to work in pairs to solve the problem. Then bring the class together for another whole-class discussion. Ask:

A + A < 20 A>5

3) 2 is a factor of

A

4) 3 is not a factor of

A

I’ll start with Clue 1. I’ll begin making a list of numbers for A .

Algebra Readiness Made Easy: Gr. 4 © 2008 by Greenes, Findell & Cavanagh, Scholastic Teaching Resources

• Which remaining number fits Clue 4? (8)

A.

CLUES:

• What does Clue 3 mean? (A is an even number. When you divide A by 2, you get a whole number for an answer.) • Which numbers does Clue 3 eliminate? (7 and 9)

What is the number on the player’s jersey?

1. What are all the numbers on Ima’s list? ___________________________

9 8

___________________________

Ima Thinker 2. What is

A? __________

3. How did you figure out the number on the jersey? ______________________________________________________ ______________________________________________________ 4. Check your number with the clues. Show your work here.

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MAKE THE CASE


The letter B stands for the number on the jersey. Use the clues to figure out

B.

CLUES:

B B < 90 – 40 B is not an even number

1) 5 is a factor of

• Who has the right answer? (Wally Walrus)

2) 3)

4) The tens digit is one less than the ones digit

• How do you think Marlee Marlin got the answer, 35? (35 fits clues 1, 2, and 3. Marlee Marlin probably forgot to use Clue 4.)

I am certain that B is 35.

I believe that B is 45.

Marlee Marlin

Obviously B is 43.

Wally Walrus 34

Who is sharp as a tack?

• How do you think Ralph Rhino got the answer 43? (43 fits clues 2, 3, and 4. Ralph Rhino probably forgot to use Clue 1.) 32


Ralph Rhino


• How did you figure it out? (From Clue 2, B is less than 90 – 40, or 50. So B can be 49 or less. Make a list of those numbers. From Clue 1, B has to have a factor of 5, so eliminate all numbers except for 5, 10, 15, 20, 25, 30, 35, 40, and 45. Clue 3 eliminates all even numbers leaving 5, 15, 25, 35, and 45. Clue 4 indicates that the tens digit is one less than the ones digit. Only 45 fits that clue.)


SOLVE THE PROBLEM


The letter A stands for the number on the jersey. Use the clues to figure out

A.

CLUES: 1) 2)

A + A < 20 A>5

3) 2 is a factor of

A

4) 3 is not a factor of

A


I’ll start with Clue 1. I’ll begin making a list of numbers for A .

1. What are all the numbers on Ima’s list? ___________________________

9 8

___________________________

Ima Thinker 2. What is

A ? __________


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MAKE THE CASE


The letter B stands for the number on the jersey. Use the clues to figure out

B.

CLUES: 1) 5 is a factor of 2) 3)

B

B < 90 – 40 B is not an even number



Marlee Marlin

Obviously B is 43.

Wally Walrus 34


Ralph Rhino




PROBLEM

1

What is the number on the player’s jersey? C stands for the number on the jersey. Use the clues to figure out C . The letter

CLUES: 1) 2)

C < 6 + 10 C is an odd number

3) 5 is not a factor of 4) 3 is a factor of 5)

C

C

C

is not 3 x 3


I’ll start with Clue 1. I’ll begin making a list of numbers less than 16. 1. Why did Ima start with Clue 1? ___________________________

15 14

___________________________ 2. What is

C ? __________

Ima Thinker

3. How did you figure out the number on the jersey? ________________________________________________________ ________________________________________________________ 4. Check your number with the clues. Show your work here.

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PROBLEM

2

What is the number on the player’s jersey? The letter D stands for the number on the jersey. Use the clues to figure out

D.

CLUES: 1) 3 is a factor of 2) 3) 4) 5)

D

D >9–4 D is not an even number D < 18 D is not 2 x 2 + 5

I’ll start with Clue 4. I’ll begin making a list of numbers less than 18.

_____________________________

17 16

_____________________________ 2. What is

D ? __________

Ima Thinker


36


1. Why did Ima start with Clue 4?


PROBLEM

3

What is the number on the player’s jersey? The letter E stands for the number on the jersey. Use the clues to figure out

E.

CLUES: 1) 2) 3) 4) 5)

E > 10 – 8 E is not an even number E + E + E < 24 3 is not a factor of E E is not 1 x 5


I’ll start with Clue 3. I’ll begin making a list of numbers less than 8.

1. Why did Ima start with Clue 3? ____________________________

7 6

____________________________ 2. What is

E ? __________

Ima Thinker


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PROBLEM

4

What is the number on the player’s jersey? The letter F stands for the number on the jersey. Use the clues to figure out

F.

CLUES: 1) 2) 3) 4)

F + F < 20 F + F + F > 12 F is not an odd number 3 is not a factor of F

1. Which clue did you use first? Why? __________________________

2. What is

F ? __________


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______________________________________________________


PROBLEM

5

What is the number on the player’s jersey? The letter G stands for the number on the jersey. Use the clues to figure out

G.

CLUES: 1) 2) 3) 4)

G > 20 G < 30 G is an odd number 3 is a factor of G

5) The difference between the tens digit and the ones digit of

G is 1


1. Which clue did you use first? Why? __________________________ ______________________________________________________ 2. What is

G ? __________


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PROBLEM

6

What is the number on the player’s jersey? The letter H stands for the number on the jersey. Use the clues to figure out

H.

CLUES: 1) 4 x

H > 40

2) 3 is a factor of 3) 4)

H

H is not an odd number H < 40 ÷ 2

5) The sum of the digits of

H is not 9

1. Which clue did you use first? Why? __________________________

2. What is

H ? __________


40


______________________________________________________


PROBLEM

7

What is the number on the player’s jersey? The letter J stands for the number on the jersey. Use the clues to figure out

J.

CLUES: 1) 2)

J > 20 J < 10 + 30 J is greater than the tens digit 5 is a factor of J The sum of the digits of J is an even number

3) The ones digit of 4) 5)


1. Which clue did you use first? Why? __________________________ ______________________________________________________ 2. What is

J ? __________


41

ALGE B

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Weigh In Overview

Students examine three scales, each showing the total weight of kids, animals, and other objects, then solve for the weight of each.

Algebra Solve two or three equations with two or three unknowns • Replace unknowns with their values

Problem-Solving Strategies Reason deductively • Test cases

Related Math Skills Compute with whole numbers

Math Language Pounds • Scale • Weigh • Total weight

Introducing the Problem Set Make photocopies of “Solve the Problem: Weigh In” (page 44) and distribute to students. Have students work in pairs, encouraging them to discuss strategies they might use to solve the problem. You may want to walk around and listen in on some of their discussions. After a few minutes, display the problem on the board (or on the overhead if you made a transparency) and use the following questions to guide a whole-class discussion on how to solve the problem: • Look at the three scales. Who are on scale A? (Tom and Smudge the cat) • Who is on scale B? (Tom) • Who are on scale C? (Tom and Alex the dog) • Whose weight do you know for sure? (Tom’s weight) How do you know? (He is the only one on scale B.) 42


WEIGH IN

Name _____________________________________________ Date __________________ WEIGH IN

SOLVE THE PROBLEM

How much does each one weigh?

• How can knowing that Tom weighs 85 pounds help you figure out Smudge’s weight? (If Tom weighs 85 pounds, and the total weight of Tom and Smudge is 100 pounds, then Smudge must weigh 100 – 85, or 15 pounds.) • How can you figure out Alex’s weight? (On scale C, Tom and Alex weigh a total of 125 pounds. Since Tom weighs 85 pounds, Alex weighs 125 – 85, or 40 pounds)

Scale C

Scale B

Scale A


I know how much Tom weighs. I’ll write that number on all his pictures.

1. What number of pounds will Ima write

Work together as a class to answer the questions in “Solve the Problem: Weigh In.”

on Tom’s pictures? __________ 2. Alex the dog weighs __________ pounds.

Ima Thinker

3. Smudge the cat weighs __________ pounds. 4. How did you figure out the number of pounds for Smudge?

Math Chat With the Transparency Display the “Make the Case: Weigh In” transparency on the overhead. Before students can decide which character is “sharp as a tack,” they need to figure out the answer to the problem. Encourage students to work in pairs to solve the problem. Then bring the class together for another whole-class discussion. Ask:

______________________________________________________ ______________________________________________________

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MAKE THE CASE

How much does James weigh? Note: The bags of rocks weigh the same amount.

• Who has the right answer? (Ralph Rhino)

• How do you think Wally Walrus got the answer of 68 pounds? (He probably subtracted the weights of both the bag of rocks and the fishbowl, or 7 pounds, from 75 pounds.) • How do you think Marlee Marlin got the answer of 73? (She probably subtracted the weight of the bag of rocks from 75 pounds instead of subtracting the weight of one fishbowl.)

Scale C Scale A


• How did you figure it out? (On scale C, five bags of rocks weighed 10 pounds. So one bag of rocks is 10 ÷ 5, or 2 pounds. Since a bag of rocks is 2 pounds, the fishbowl on scale B is 7 – 2, or 5 pounds. Since a fishbowl weighs 5 pounds, James on scale A must weigh 75 – 5, or 70 pounds.)

Scale B

That’s easy. James is 73 pounds.

It’s clear. James weighs 68 pounds.

Marlee Marlin

No way! James weighs 70 pounds.

Wally Walrus



Ralph Rhino 45

43


SOLVE THE PROBLEM


Scale A

Scale C

Scale B

1. What number of pounds will Ima write on Tom’s pictures? __________ 2. Alex the dog weighs __________ pounds.

Ima Thinker

3. Smudge the cat weighs __________ pounds. 4. How did you figure out the number of pounds for Smudge? ______________________________________________________ ______________________________________________________

44


I know how much Tom weighs. I’ll write that number on all his pictures.


MAKE THE CASE


Scale C


Scale A

Scale B



Marlee Marlin


Wally Walrus


Ralph Rhino 45


PROBLEM

1


Scale A

Scale B

Scale C

1. What number of pounds will Ima write on Lancelot’s pictures? __________ 2. Gwen the duck weighs __________ pounds.

Ima Thinker

3. Sue weighs __________ pounds. 4. How much do Sue, Lancelot, and Gwen weigh altogether? __________

46


I know how much Lancelot weighs. I’ll write that number on all his pictures.


PROBLEM

2



Scale A

Scale C

Scale B

I know how much Daniel weighs. I’ll write that number on all his pictures.

1. What number of pounds will Ima write on the pictures of Daniel? __________ 2. Lisa weighs __________ pounds.

Ima Thinker

3. Sly the snake weighs __________ pounds. 4. How much more does Daniel weigh than Lisa? __________

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PROBLEM

3


Scale A

Scale B

Scale C

1. What number of pounds will Ima write on the pictures of Jenna? __________ 2. Keisha weighs __________ pounds.

Ima Thinker

3. Sasha the dog weighs __________ pounds. 4. Altogether, Jenna, Keisha, and Sasha weigh __________ pounds.

48


I know how much Jenna weighs. I’ll write that number on all her pictures.


PROBLEM

4



Scale A

Scale B

Scale C

1. Billy the goat weighs __________ pounds. 2. Nancy weighs __________ pounds. 3. Horace the rabbit weighs __________ pounds. 4. How much more does Billy weigh than Horace? __________

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PROBLEM

5


Scale A

Scale B

Scale C

2. Tabby the cat weighs __________ pounds. 3. Winslow the rabbit weighs __________ pounds. 4. How did you figure out how much Winslow weighs? ______________________________________________________ ______________________________________________________

50


1. One cage weighs __________ pounds.


PROBLEM

6



Scale A

Scale B

Scale C

1. One bag of dog food weighs __________ pounds. 2. Bowser the dog weighs __________ pounds. 3. Mario weighs __________ pounds. 4. How did you figure out how much Mario weighs? ______________________________________________________ ______________________________________________________

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PROBLEM

7


Scale A

Scale B

Scale C

2. One bag of cat food weighs __________ pounds. 3. El Gato the cat weighs __________ pounds. 4. How did you figure out how much El Gato weighs? ______________________________________________________ ______________________________________________________

52


1. One box of cat litter weighs __________ pounds.

ALGE B

Balancing Animals

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Overview Shown two pan balances with toy animals, students identify how many of one type of toy animal will balance another type of toy animal.

Algebra Understand that substituting one set of animals with a second set of equal weight preserves balance • Explore equality through the use of pan balances

Problem-Solving Strategies Reason about proportional relationships

Related Math Skills Compute with whole numbers

Math Language Balance •

Weigh the same

Introducing the Problem Set Make photocopies of “Solve the Problem: Balancing Animals” (page 55) and distribute to students. Have students work in pairs, encouraging them to discuss strategies they might use to solve the problem. You may want to walk around and listen in on some of their discussions. After a few minutes, display the problem on the board (or on the overhead if you made a transparency) and use the following questions to guide a whole-class discussion on how to solve the problem: • Look at the pan balances. What do you see? (Two pan balances that show equal weights. The first pan balance shows that 2 fish balance one frog. The second pan balance shows that 3 frogs balance one shark.) • Which weighs more—one frog or one fish? (One frog) How do you know? (It takes 2 fish to balance one frog, so the frog weighs twice as much as one fish, or one fish is half the weight of one frog.) Algebra Readiness Made Easy: Grade 4 © Greenes, Findell & Cavanagh, Scholastic Teaching Resources

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BALANCING ANIMALS

READ I RA

Name _____________________________________________ Date __________________ BALANCING ANIMALS

SOLVE THE PROBLEM

How many fish will balance one shark?

• What do you need to figure out? (How many fish will balance one shark?) • What will you do first? (Write “2 fish” on each frog in the second pan balance.) • If one frog weighs 2 pounds, how many pounds is one shark? (6 pounds) How do you know? (3 frogs balance one shark, and 2 + 2 + 2 = 6)

Math Chat With the Transparency Display the “Make the Case: Balancing Animals” transparency on the overhead. Before students can decide which character is “sharp as a tack,” they need to figure out the answer to the problem. Encourage students to work in pairs to solve the problem. Then bring the class together for another whole-class discussion. Ask: • Who has the right answer? (Wally Walrus)

I know how many fish balance one frog. I’ll write that number of fish on each frog.


Work together as a class to answer the questions in “Solve the Problem: Balancing Animals.”

Toy animals that are the same weigh the same.

1. What number of fish will Ima write on each frog? __________

Ima Thinker

2. How many frogs balance one shark? ________ 3. How many fish will balance one shark? ________ 4. How did you figure out the answer to #3

_____________________

______________________________________________________

55


MAKE THE CASE

How many crabs will balance one lobster?

• How did you figure it out? (One crab balances 3 clams, so 2 crabs will balance 6 clams. Since 6 clams balance 1 lobster, 2 crabs balance 1 lobster.) • How do you think Marlee Marlin got the answer 3? (She probably mixed up crabs and clams, and forgot to multiply the 3 clams by 2.)


Obviously it’s 3 crabs.

• How do you think Ralph Rhino got the answer 18? (He probably multiplied 3 times the number of clams in the second pan: 3 x 6 = 18.)

Marlee Marlin You’re both wrong. I am sure it’s 18 crabs.

Wally Walrus 56

54



Ralph Rhino


That’s easy. Two crabs will balance one lobster.


SOLVE THE PROBLEM

How many fish will balance one shark?



I know how many fish balance one frog. I’ll write that number of fish on each frog.

1. What number of fish will Ima write on each frog? __________

Ima Thinker

2. How many frogs balance one shark? ________ 3. How many fish will balance one shark? ________ 4. How did you figure out the answer to #3

_____________________

______________________________________________________

55


MAKE THE CASE




Marlee Marlin You’re both wrong. I am sure it’s 18 crabs.

Wally Walrus 56


Ralph Rhino




PROBLEM

1

How many cats will balance one cow?



I know how many cats balance two pigs. I’ll write that number of cats on each set of two pigs.

1. What number of cats will Ima write on each set of two pigs? __________

Ima Thinker

2. How many pigs balance one cow? __________ 3. How many cats will balance one cow? __________ 4. How did you figure out the answer to #3? _____________________ ______________________________________________________

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PROBLEM

2

How many pigs will balance one horse?


1. How many goats balance 2 pigs? __________ 2. How many pigs will balance one horse?

Ima Thinker

__________ 3. How did you figure out the answer to #2? _____________________ ______________________________________________________ 4. If one goat weighs 2 pounds, what is the weight of one horse? __________ 58


I know how many pigs balance 2 goats. I’ll write that number of pigs on each set of 2 goats.


PROBLEM

3

How many rabbits will balance one lamb?



1. How many rabbits balance one monkey? __________ 2. How many rabbits will balance one lamb? __________ 3. How did you figure out the answer to #2? ______________________ ______________________________________________________ 4. If one monkey weighs 4 pounds, what is the weight of one lamb? __________

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PROBLEM

4

How many birds will balance one dog?


2. How many birds will balance one dog? __________ 3. How did you figure out the answer to #2? _____________________ ______________________________________________________ 4. If one bird weighs 1 pound, what is the weight of one dog? __________

60


1. How many cats balance one dog? __________


PROBLEM

5

How many giraffes will balance one elephant?



1. How many camels balance one giraffe? __________ 2. How many giraffes will balance one elephant? __________ 3. How did you figure out the answer to #2? _____________________ ______________________________________________________ 4. If one giraffe weighs 6 pounds, what is the weight of one elephant? __________

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PROBLEM

6

How many snakes will balance one rabbit?


2. How many snakes will balance one rabbit? __________ 3. How did you figure out the answer to #2? _____________________ ______________________________________________________ 4. If one snake weighs 3 pounds, what is the weight of one rabbit? __________

62


1. How many turtles balance one snake? __________


PROBLEM

7

How many kittens will balance one puppy?



1. How many mice balance one puppy? __________ 2. How many kittens will balance one puppy? __________ 3. How did you figure out the answer to #2? _____________________ ______________________________________________________ 4. If one puppy weighs 12 pounds, what is the weight of one kitten? __________

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ALGE B

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Where’s My Seat? Overview

Presented with a rectangular array of consecutive numbers, students identify the relationship between row numbers and seat numbers in the rows.

Algebra Explore variables as representing varying quantities • Describe the functional relationship between the last number in a row and the row number • Describe the functional relationship between an element in a row and elements directly above and below it

Problem-Solving Strategies Describe parts of patterns • Generalize pattern relationships

Related Math Skills Compute with counting numbers

Math Language Row • Spatial terminology: behind, in front of, next to, first (seat), last (seat)

Introducing the Problem Set Make photocopies of “Solve the Problem: Where’s My Seat?” (page 66) and distribute to students. Have students work in pairs, encouraging them to discuss strategies they might use to solve the problem. You may want to walk around and listen in on some of their discussions. After a few minutes, display the problem on the board (or on the overhead if you made a transparency) and use the following questions to guide a whole-class discussion on how to solve the problem: • What is the last number in Row 1? (5) Row 2? (10) Row 5? (25) • How can you figure out the last number in a row? (Count the row numbers by 5s or multiply 5 x row number) 64


WHERE’S MY SEAT?

Name _____________________________________________ Date __________________ WHERE’S MY SEAT?

SOLVE THE PROBLEM

I’m sitting in the last seat in Row 8. What is my seat number?

There are 20 rows of seats like these.

• What is Carl’s seat number? (40) How do you know? (The last number of Row 8 is 5 x 8, or 40) • Where is Alphonse sitting? (First seat in Row 10) How can you figure out the number of the first seat in Row 10? (It is one more than the last seat in Row 9, or 5 x 9 + 1 = 46)

ROW 6

.

.

.

.

.

ROW 5

21

22

.

.

.

ROW 4

16

17

18

19

20

ROW 3

11

12

13

14

15

ROW 2

6

7

8

9

10

ROW 1

1

2

3

4

5

STAGE Carl

Work together as a class to answer the questions in “Solve the Problem: Where’s My Seat?”


The last seat in Row 1 is 5. The last seat in Row 2 is 10. The last seat in Row 3 is 15. I see a pattern.

• What is Peter’s seat number? (41) How did you figure it out? (46 – 5 = 41)

1. What pattern did Ima see? ____________ _________________________________

Ima Thinker 2. Carl is in seat __________ . 3. Alphonse is sitting in the first seat in Row 10. Alphonse is in seat

Math Chat With the Transparency Display the “Make the Case: Where’s My Seat?” transparency on the overhead. Before students can decide which character is “sharp as a tack,” they need to figure out the answer to the problem. Encourage students to work in pairs to solve the problem. Then bring the class together for another whole-class discussion. Ask:

__________ . 4. Peter is sitting in the seat right in front of Alphonse. Peter is in seat __________ .

66


MAKE THE CASE

I’m sitting in Row 8. My seat is next to the first seat in the row. What is my seat number? There are 10 rows of seats like these. Olivia

• Who has the right answer? (Marlee Marlin) • How did you figure it out? (The last seat in Row 7 is 70. The first seat in Row 8 is 71. The seat next to 71 is 72.)

• How do you think Ralph Rhino got the answer of 71? (He probably didn’t read the whole problem. He got the number of the first seat of the row, but forgot to get the number of the seat next to the first seat.)

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31

32

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ROW 1

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STAGE


• How do you think Wally Walrus got the answer 82? (He probably thought that all of the seats in Row 8 have numbers in the 80s. So the first seat is 81 and the one next to it is 81 + 1, or 82.)

ROW 5

72 is the right answer. I just know it.

That’s easy. She is in seat 82.

Marlee Marlin

No way. It has to be seat 71.

Wally Walrus



Ralph Rhino 67

65


SOLVE THE PROBLEM


There are 20 rows of seats like these. ROW 6

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ROW 1

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5

STAGE Carl

1. What pattern did Ima see? ____________ _________________________________

Ima Thinker 2. Carl is in seat __________ . 3. Alphonse is sitting in the first seat in Row 10. Alphonse is in seat __________ . 4. Peter is sitting in the seat right in front of Alphonse. Peter is in seat __________ .

66




MAKE THE CASE

I’m sitting in Row 8. My seat is next to the first seat in the row. What is my seat number? There are 10 rows of seats like these. Olivia ROW 5

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STAGE



Marlee Marlin


Wally Walrus


Ralph Rhino 67


PROBLEM

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STAGE Jeffrey

1. What pattern did Ima see? ______________ ___________________________________

Ima Thinker

2. Jeffrey is in seat __________ . 3. Frida is sitting right behind Jeffrey. Frida is in seat __________ . 4. Theo is sitting next to Frida. Theo is in seat __________ .

68




PROBLEM

2


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STAGE


Penny


1. What pattern did Ima see? _______________ ____________________________________

Ima Thinker

2. Penny is in seat __________ . 3. Zach is sitting next to Penny. Zach is in seat __________ . 4. Felipe is sitting right in front of Zach. Felipe is in seat __________ .

69


PROBLEM

3 There are 20 rows of seats like these. ROW 5

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STAGE

Jeremy

The last seat in Row 1 is 8. The last seat in Row 2 is 16. The last seat in Row 3 is 24.

1. What pattern did Ima see? ______________ ___________________________________

Ima Thinker

2. Jeremy is sitting in seat __________ . 3. Dina is sitting next to Jeremy. Dina is in seat __________ . 4. Logan is sitting in the first seat in Row 10. Logan is in seat __________ .

70


I see a pattern.


PROBLEM

4


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STAGE


Helena

1. Helena is sitting in seat __________ . 2. Ginny is sitting in the first seat in Row 7. Ginny is in seat _________ . 3. Tomas is sitting right in front of Ginny. Tomas is in Row __________ and his seat number is __________ . 4. Leo is sitting right in front of Tomas. Leo is in Row __________ and his seat number is __________ .

71


PROBLEM

5

My seat is next to the last seat of Row 7. What is my seat number? There are 20 rows of seats like these.

Stefan

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STAGE

2. A.J. sat two rows directly in front of Stefan. A.J. sat in Row ________ and seat __________. 3. Charlie sat in seat 93. Charlie was in Row __________. 4. How did you figure out Charlie’s row number? ___________________ ______________________________________________________

72


1. Stefan is sitting in seat __________.


PROBLEM

6 There are 20 rows of seats like these. ROW 6

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My seat is the middle seat in Row 6. What is my seat number?

STAGE


Katya

1. Katya is sitting in seat __________. 2. Doug sat directly behind Katya. Doug is in Row __________ and seat __________. 3. Jimmy sat two rows directly behind Doug. Jimmy is in Row _________ and seat _________ . 4. How did you figure out Jimmy’s seat number? ___________________ ______________________________________________________

73


PROBLEM

7


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I’ll go to the first seat in Row 9 and sit down. What is my seat number?

6

STAGE Stella

2. Ally sat right next to Stella. Ally is in seat __________. 3. Samantha sat right in front of Ally. Samantha is in Row _________ and seat __________. 4. How did you figure out Samantha’s seat number? _________________ ______________________________________________________

74


1. Stella is sitting at seat __________.

PROBLEM-SOLVING TRANSPARENCY


SOLVE IT

1.

Look

2.

Plan and Do

3.

Answer and Check

What is the problem?

What will you do first? How will you solve the problem?

How can you be sure your answer is correct?

SOLVE IT: DOG DATA

How much is each dog’s doctor bill?

Spot

Windy Day

DeVine

Holly Wood

Use the facts to figure out the doctor’s bill for each dog. FACTS: A Spot’s bill was twice as much as Windy Day’s bill. B Windy Day’s bill was $50 more than DeVine’s bill. C DeVine’s bill was 1/3 of Holly Wood’s bill. D Holly Wood’s bill was $30.

SOLVE IT: STAMP STUMPERS

How much is one cone stamp? The total cost of the four stamps on the envelope is 49¢. The cone stamps cost the same.

4 stamps Total cost . . . 49¢

76 Algebra Readiness Made Easy: Grade 4 © Greenes, Findell & Cavanagh, Scholastic Teaching Resources

SOLVE IT: JERSEY NUMBER

What is the number on the player’s jersey? K stands for the number on the jersey. Use the clues to figure out K .

The letter

CLUES: 1) 2 x

K > 18

2) 4 is a factor of

K

3) The tens digit is one more than the ones digit 4)

K < 100 – 60

SOLVE IT: WEIGH IN

How much does Maria the pig weigh?

Scale A

Scale B

Scale C


SOLVE IT: BALANCING ANIMALS

How many monkeys will balance one elephant?


SOLVE IT: WHERE’S MY SEAT?

Henry is sitting in the first seat in Row 7. I’m sitting next to Henry. What’s my seat number?

There are 20 rows of seats like these.

Kayla

ROW 4

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STAGE


ANSWER KEY Dog Data (pages 11–19) Solve the Problem 1. Fact C 2. 12 3. 15 4. Work backward. Fact C: Holly Wood is 6 years old. Fact B: Ms. Clean is 2 x 6, or 12 years old. Fact A: Popeye is 12 + 3, or 15 years old. Make the Case Who is sharp as a tack? Marlee Marlin Problem 1 1. Fact C 2. 7 years old 3. 2 years old 4. Work backward. Fact C: Bubba is 14 years old. Fact B: DeVine is ¹⁄₂ of 14, or 7 years old. Fact A. Howdy is 7 – 5, or 2 years old. Problem 2 1. Fact D 2. 48 pounds 3. 38 pounds 4. Work backward. Fact D: Windy Day weighs 24 pounds. Fact C: Dandy weighs 2 x 24, or 48 pounds. Fact B: Bubba weighs 48 – 10, or 38 pounds. Fact A: Melody weighs 38 – 4, or 34 pounds. Problem 3 1. Fact D 2. 50 pounds 3. 25 pounds 4. Work backward. Fact D: Madam Peppy weighs 5 pounds. Fact C: DeVine weighs 10 x 5, or 50 pounds. Fact B: Popeye is ¹⁄₂ of 50, or 25 pounds. Fact A: Spot is 25 – 4, or 21 pounds. Problem 4 1. Fact D 2. 38 pounds 3. 55 pounds 4. Work backward. Fact D: Ms. Clean weighs 19 pounds. Fact C: Holly Wood weighs 2 x 19, or 38 pounds. Fact B: Howdy weighs 38 + 17, or 55 pounds. Fact A: Betsy weighs 55 – 10, or 45 pounds.

Problem 7 1. Fact D 2. $80 3. $90 4. Work backward. Fact D: Ms. Clean’s bill was $40. Fact C: Madam Peppy’s bill was 2 x $40, or $80. Fact B: Dandy’s bill was $80 + $10, or $90. Fact A: Betsy’s bill was $150 – $90, or $60. Solve It: Dog Data 1. Look: Facts are given about the doctor bills for four dogs. Fact D about Holly Wood’s bill is the only cost known. To figure out DeVine’s bill, we need to use Holly Wood’s bill. For Windy Day’s bill, we need to know DeVine’s bill. For Spot’s bill, we need to know Windy Day’s bill 2. Plan and Do: Work backward. Fact D: Holly Wood’s bill was $30. Fact C: DeVine’s bill was ¹⁄₃ of $30, or $10. Fact B: Windy Day’s bill was $50 + $10, or $60. Fact A: Spot’s bill was 2 x $60, or $120. 3. Answer and Check: Spot’s bill was $120, Windy Day’s bill was $60, De Vine’s bill was $20, and Holly Wood’s bill was $30. To check, use the amounts of the bills for each dog and check against the facts. Do they make sense? DeVine’s bill: $10, which is ¹⁄₃ of Holly Wood’s $30 bill. Windy Day’s bill: $60, which is $50 more than DeVine’s bill of $10. Spot’s bill: $120, which is 2 x Windy Day’s $60 bill. Stamp Stumpers (pages 22–30) Solve the Problem 1. By taking away the 5¢ stamp from the envelope and subtracting 5¢ from the total cost, the amount left would be the cost of the four chevron stamps 2. 13¢ – 5¢ = 8¢ 3. 2¢ 4. When you take away the 5¢ stamp, the total cost changes to 13¢ – 5¢, or 8¢. So the four chevron stamps cost 8¢. One chevron stamp is 8¢ ÷ 4, or 2¢. Make the Case Who is sharp as a tack? Ralph Rhino

Problem 5 1. Fact D 2. 9 ounces 3. 17 ounces 4. Work backward. Fact D: Howdy eats 18 ounces of food. Fact C: Ms. Clean eats ¹⁄₂ x 18, or 9 ounces. Fact B: Dandy eats 9 + 8, or 17 ounces. Fact A: Spot eats 17 – 2, or 15 ounces.

Problem 1 1. By taking the 2¢ stamp off the envelope and subtracting 2¢ from the total cost, the amount left is the cost of the three octagon stamps. 2. 17¢ – 2¢ = 15¢ 3. 5¢ 4. When you take away the 2¢ stamp, the total cost changes to 17¢ – 2¢, or 15¢. So the three octagon stamps cost 15¢. That means that one octagon stamp is 15¢ ÷ 3, or 5¢.

Problem 6 1. Fact D 2. 12 ounces 3. 3 ounces 4. Work backward. Fact D: Windy Day eats 8 ounces of food. Fact C: Popeye eats 20 – 8, or 12 ounces. Fact B: Madam Peppy eats ¹⁄₄ of 12, or 3 ounces. Fact A: Melody eats 6 + 3, or 9 ounces.

Problem 2 1. By taking the 3¢ stamp off the envelope and subtracting 3¢ from the total cost, the amount left is the cost of the three pentagon stamps. 2. 10¢ 3. 33¢ – 3¢ = 30¢; 30¢ ÷ 3 = 10¢ 4. 30¢

Problem 3 1. By taking the 8¢ stamp off the envelope and subtracting 8¢ from the total cost, the number left is the cost of the three triangle stamps. 2. 7¢ 3. 29¢ – 8 = 21¢; 21¢ ÷ 3 = 7¢ 4. 30¢ Problem 4 1. 6¢ 2. 25¢ – 1¢ = 24¢; 24¢ ÷ 4 = 6¢ 3. 20¢ 4. 8¢ Problem 5 1. 3¢ 2. 15¢ – 3¢ = 12¢; 12¢ ÷ 4 = 3¢ 3. 16¢ 4. 5¢ Problem 6 1. 8¢ 2. 31¢ – 2¢ – 5¢ = 24¢; 24¢ ÷ 3 = 8¢ 3. 28¢ 4. 9¢ Problem 7 1. 9¢ 2. 40¢ – 4¢ = 36¢; 36¢ ÷ 4 = 9¢ 3. 47¢ 4. 20¢ Solve It: Stamp Stumpers 1. Look: There are four stamps on the envelope and a receipt that shows the total cost of 49¢. There are three cone stamps and one 4¢ stamp. The problem is to figure out the cost of one cone stamp. 2. Plan and Do: First, pretend to take the 4¢ stamp off the envelope and subtract 4¢ from the total cost. That means that the cost of the three cone stamps is 49¢ – 4¢, or 45¢. Divide 45¢ by 3 to get the value of one cone stamp. 3. Answer and Check: Each stamp is 45¢ ÷ 3, or 15¢. To check, record 15¢ on each cone and add the costs: 15¢ + 4¢ + 15¢ + 15¢ = 49¢. This sum matches the total cost. Jersey Number (pages 33–41) Solve the Problem 1. 9, 8, 7, 6, 5, 4, 3, 2, 1, and 0 2. A = 8 3. Possible answer: From Clue 1, A is 9 or less. Make a list of those numbers. Clue 2 eliminates 0 through 5, leaving 6, 7, 8, and 9. Clue 3 eliminates 7 and 9, leaving 6 and 8. Clue 4 eliminates 6. So, A is 8. 4. Replace A with 8. Check 8 with each clue: 8 + 8 < 20, 8 > 5, 2 is a factor of 8, and 3 is not a factor of 8. Make the Case Who is sharp as a tack? Wally Walrus Problem 1 1. Clue 1 gives the greatest number that C can be. C is 15 or less. 2. C = 3 3. Possible answer: Clue 1 gives the list of numbers 0 through 15. Clue 2 eliminates all even numbers. Clue 3 eliminates 5 and 15. Clue 4 eliminates all numbers except for 3 and 9. Clue 5 eliminates 9. So, C is 3. 4. Replace C with 3. Check 3 with each clue.

Problem 2 1. Clue 4 gives the greatest number that D can be. D is 17 or less. 2. D = 15 3. Possible answer: Clue 4 gives D as 17 or less. List the numbers 0 through 17. Clue 2 eliminates zero through 5. Clue 3 eliminates all even numbers. Clue 1 eliminates 7, 11, 13, and 17. Clue 5 eliminates 9. So, D is 15. 4. Replace D with 15. Check 15 with each clue. Problem 3 1. Clue 3 gives the greatest number that E can be. E is 7 or less. 2. E = 7 3. Possible answer: Clue 3 gives the list of numbers 0 through 7. Clue 1 eliminates 0, 1, and 2. Clue 2 eliminates 4 and 6. Clue 4 eliminates 3. Clue 5 eliminates 5. So, E is 7. 4. Replace E with 7. Check 7 with each clue. Problem 4 1. Clue 1 gives the greatest number that F can be. F is 9 or less. 2. F = 8 3. Possible answer: Clue 1 gives the list of numbers 0 through 9. Clue 2 eliminates all numbers less than 5. Clue 3 eliminates all odd numbers. Clue 4 eliminates 6. So, F is 8. 4. Replace F with 8. Check 8 with each clue. Problem 5 1. Clue 2 gives the greatest number that G can be. G is 29 or less. 2. G = 21 3. Possible answer: Clue 2 gives the list of numbers 0 through 29. Clue 1 eliminates all numbers 20 and less. Clue 3 eliminates all even numbers. Clue 4 eliminates all numbers except for 21 and 27. Clue 5 eliminates 27. So, G is 21. 4. Replace G with 21. Check 21 with each clue. Problem 6 1. Clue 4 gives the greatest number that H can be. H is 19 or less. 2. H = 12 3. Possible answer: Clue 4 gives the list of numbers 0 through 19. Clue 1 eliminates all numbers 10 and less. Clue 3 eliminates all odd numbers. Clue 2 eliminates 14 and 16. Clue 5 eliminates 18. So, H is 12. 4. Replace H with 12. Check 12 with each clue. Problem 7 1. Clue 2 gives the greatest number that J can be. J is 39 or less. 2. J = 35 3. Possible answer: Clue 2 gives the list of numbers 0 through 39. Clue 1 eliminates all numbers 20 and less. Clue 4 eliminates all numbers except for 25, 30, and 35. Clue 3 eliminates 30. Clue 5 eliminates 25. So, J is 35. 4. Replace J with 35. Check 35 with each clue.


79

Solve It: Jersey Number 1. Look: Four clues are given to figure out the number on the player’s jersey. The number is represented by the letter K. 2. Plan and Do: Clues 1 and 4 establish the range for K. K > 9 and K < 40, so K can be any number 10 through 39. Clue 2 indicates that 4 is a factor of K, so eliminate all numbers except for 12, 16, 20, 24, 28, 32, and 36. The only number that fits Clue 3 is 32. So, K is 32. 3. Answer and Check: K = 32. Replace K with 32. Check 32 with each clue. Weigh In (pages 44–52) Solve the Problem 1. 85 2. 40 3. 15 4. Answers will vary. Possible answer: On scale B, Tom weighs 85 pounds. On scale A, Tom and Smudge weigh 100 pounds altogether. So Smudge weighs 100 – 85, or 15 pounds. Make the Case Who is sharp as a tack? Ralph Rhino Problem 1 1. 7 2. 8 3. 65 4. 80 pounds Problem 2 1. 67 2. 43 3. 4 4. 24 pounds

Solve It: Weigh In 1. Look: Three scales A, B, and C. On A, Peter and one box of dog bones are 66 pounds. On B, Peter and Maria the pig are 77 pounds. On C, 3 boxes of dog bones are 18 pounds. The problem is to figure out how much Maria weighs. 2. Plan and Do: On scale C, one box of dog bones is 18 ÷ 3, or 6 pounds. On scale A, the box of dog bones is 6 pounds, so Peter is 66 – 6, or 60 pounds. On scale B, since Peter is 60 pounds, then Maria the pig is 77 – 60, or 17 pounds. 3. Answer and Check: Maria is 17 pounds. To check, replace each box of dog bones with 6 pounds, Peter with 60 pounds, and Maria with 17 pounds, and figure out the sum of the weight on each scale. The sums should match the numbers of pounds shown on the scales. Balancing Animals (pages 55–63) Solve the Problem 1. 2 fish 2. 3 frogs 3. 6 fish 4. Two fish balance 1 frog, so 6 fish will balance 3 frogs. That means 6 fish will balance 1 shark.

Problem 3 1. 80 2. 75 3. 40 4. 195

Make the Case Who is sharp as a tack? Wally Walrus

Problem 4 1. 18 2. 90 3. 10 4. 8 pounds Problem 5 1. 12 2. 13 3. 7 4. Answers may vary. Possible answer: The cage and Tabby are 25 pounds. Winslow weighs 32 – 25, or 7 pounds. Problem 6 1. 15 2. 35 3. 70 4. Answers may vary. Possible answer: Bowser and one bag of food weigh 50 pounds on scale A. Since Bowser and one bag of food is 50 pounds, then on scale B, Mario is 120 – 50, or 70 pounds.

80

Problem 7 1. 10 2. 9 3. 14 4. Answers may vary. Possible answer: On scale B, one box of cat litter is 20 ÷ 2, or 10 pounds. On scale C, one bag of cat food is 27 ÷ 3, or 9 pounds. On scale A, the box of cat litter and the bag of cat food are 10 + 9, or 19 pounds. So, El Gato the cat is 33 – 19, or 14 pounds.

Problem 1 1. 1 cat 2. 4 pigs 3. 2 cats 4. One cat balances 2 pigs, so 2 cats will balance 4 pigs. That means 2 cats will balance 1 cow. Problem 2 1. 2 goats 2. 4 pigs 3. Two goats balance 2 pigs, so 4 goats will balance 4 pigs. That means 4 pigs will balance 1 horse. 4. 8 pounds Problem 3 1. 2 rabbits 2. 8 rabbits 3. Two rabbits balance 1 monkey, so 8 rabbits will balance 4 monkeys. That means 8 rabbits will balance 1 lamb. 4. 16 pounds Problem 4 1. 3 cats 2. 12 birds 3. Four birds balance 1 cat, so 12 birds will balance 3 cats. That means 12 birds will balance one dog. 4. 12 pounds

Problem 5 1. 2 camels 2. 3 giraffes 3. One giraffe balances 2 camels, so 3 giraffes will balance 6 camels. That means 3 giraffes will balance one elephant. 4. 18 pounds Problem 6 1. 3 turtles 2. 3 snakes 3. One snake balances 3 turtles, so 3 snakes will balance 9 turtles. That means 3 snakes will balance 1 rabbit. 4. 9 pounds Problem 7 1. 12 mice 2. 4 kittens 3. Three mice balance 1 kitten, so 12 mice will balance 4 kittens. That means 4 kittens will balance 1 puppy. 4. 3 pounds Solve It: Balancing Animals 1. Look: There are two pan balances. On the first pan balance, 2 monkeys balance 1 lion. On the second pan balance, 5 lions balance 1 elephant. The problem is to figure out how many monkeys will balance one elephant. 2. Plan and Do: One lion balances 2 monkeys, so 5 lions will balance 10 monkeys. That means 10 monkeys will balance 1 elephant. 3. Answer and Check: 10 monkeys will balance one elephant. To check, write the number of monkeys on each lion and count the monkeys. There should be 10. Where’s My Seat? (pages 66–74) Solve the Problem 1. The number of the last seat in a row is 5 times the row number. 2. 40 3. 46 4. 41

Problem 5 1. 69 2. Row 5 and seat 49 3. Row 10 4. Answers may vary. Possible answer: The last seat in Row 9 is 9 x 10, or 90. So, 93 is in row 10. Problem 6 1. 28 2. Row 7 and seat 33 3. Row 9 and seat 43 4. Answers may vary. Possible answer: Katya is in Row 6 and seat 28. Doug is in Row 7 and seat 28 + 5, or 33. Jimmy is in Row 9 and in seat 33 + 5 + 5, or 43. Problem 7 1. 49 2. 50 3. Row 8 and seat 44 4. Answers may vary. Possible answer: The last number in Row 8 is 8 x 6, or 48. Stella is in 48 + 1, or seat 49 in Row 9. Ally is in seat 49 + 1, or 50. Samantha is in Row 8 and seat 50 – 6, or 44. Solve It: Where’s My Seat? 1. Look: Rows of numbers with 9 numbers in each row. The last number in each row is a multiple of 9 and is 9 x the row number. The problem is to figure out Kayla’s seat number. 2. Plan and Do: First figure out where Henry is sitting. The number of the last seat in Row 6 is 6 x 9, or 54. The first seat in Row 7 is 54 + 1, or 55 so Henry is in seat 55. Kayla is in seat 55 + 1, or 56. 3. Answer & Check: The answer is 56. To check, use a different solution method. The last seat in Row 7 is 7 x 9, or 63. There are 9 seats in a row. Count backward from 63 to the first seat in the row, 55. Then the seat next to the first seat is 56.

Make the Case Who is sharp as a tack? Marlee Marlin Problem 1 1. The number of the last seat in a row is 4 times the row number. 2. 24 3. 28 4. 27 Problem 2 1. The number of the last seat in a row is 3 times the row number. 2. 27 3. 26 4. 23 Problem 3 1. The number of the last seat in a row is 8 times the row number. 2. 80 3. 79 4. 73 Problem 4 1. 28 2. 25 3. Row 6 and seat 21 4. Row 5 and seat 17


KE

THE C

4

DOG DATA

E AS

MA

TEACHING TRANSPARENCY

How old are the dogs? Use the facts to figure out each dog’s age.

Madam Peppy

Dandy

Windy Day

FACTS: A Dandy’s age is twice Madam Peppy’s age. B Madam Peppy is 2 years older than Windy Day. C Windy Day is 4 years old.

Without a doubt, Dandy is 12 years old, Madam Peppy is 6 years old, and Windy Day is 4 years old.

Clearly, Dandy is 6 years old, Madam Peppy is 2 years old, and Windy Day is 4 years old.

Marlee Marlin

Wally Walrus

I’m sure that Dandy is 8 years old, Madam Peppy is 6 years old, and Windy Day is 4 years old.

Ralph Rhino

Who is sharp as a tack? Algebra Readiness Made Easy: Gr. 4 © 2008 by Greenes, Findell & Cavanagh, Scholastic Teaching Resources

81

KE

THE C

4

STAMP STUMPERS

E AS

MA


How much is one trapezoid stamp? The total cost of the five stamps on the envelope is 21¢.


The trapezoid stamps cost the same.

I’m sure it costs 6¢.

That’s easy. One trapezoid stamp costs 5¢.

Marlee Marlin

You’re both wrong. It has to be 4¢.

Wally Walrus

Ralph Rhino


82

KE

THE C

4

JERSEY NUMBER

E AS

MA


What is the number on the player’s jersey? The letter B stands for the number on the jersey. Use the clues to figure out B .

CLUES: 1) 5 is a factor of 2) 3)

B

B < 90 – 40 B is not an even number




Marlee Marlin

Obviously B is 43.

Wally Walrus

Ralph Rhino


83

KE

THE C

4

WEIGH IN

E AS

MA



Scale C Scale A Scale B



Marlee Marlin


Wally Walrus

Ralph Rhino


84

KE

THE C

4

BALANCING ANIMALS

E AS

MA






Marlee Marlin

You’re both wrong. I am sure it’s 18 crabs.

Wally Walrus

Ralph Rhino


85

KE

THE C

4

WHERE’S MY SEAT?

E AS

MA


I’m sitting in Row 8. My seat is next to the first seat in the row. What is my seat number?


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ROW 1

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3

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6

7

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STAGE



Marlee Marlin


Wally Walrus

Ralph Rhino


86

S


E I

PROBLEM - SOLVING TRANSPARENCY

T

OLV

4

1.

Look

2.

Plan and Do

3.

Answer and Check

What is the problem?

What will you do first? How will you solve the problem?

How can you be sure your answer is correct?


87


SOLVE IT: DOG DATA

How much is each dog’s doctor bill?

Spot

Windy Day

DeVine

Holly Wood

Use the facts to figure out the doctor’s bill for each dog. FACTS: A Spot’s bill was twice as much as Windy Day’s bill. B Windy Day’s bill was $50 more than DeVine’s bill. 1

C DeVine’s bill was /3 of Holly Wood’s bill. D Holly Wood’s bill was $30.


SOLVE IT: STAMP STUMPERS

How much is one cone stamp? The total cost of the four stamps on the envelope is 49¢. The cone stamps cost the same.



88


SOLVE IT: JERSEY NUMBER

What is the number on the player’s jersey? The letter K stands for the number on the jersey. Use the clues to figure out K .

CLUES: 1) 2 x

K > 18

2) 4 is a factor of

K

3) The tens digit is one more than the ones digit 4)

K < 100 – 60


SOLVE IT: WEIGH IN

How much does Maria the pig weigh?

Scale A

Scale B

Scale C


89


SOLVE IT: BALANCING ANIMALS

How many monkeys will balance one elephant?



SOLVE IT: WHERE’S MY SEAT?

Henry is sitting in the first seat in Row 7. I’m sitting next to Henry. What’s my seat number?


28

.

.

.

.

.

.

.

.

ROW 3

19

20

21

22

23

24

25

26

27

ROW 2

10

11

12

13

14

15

16

17

18

ROW 1

1

2

3

4

5

6

7

8

9

STAGE


90

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